Originally Posted by

**mark1950** $\displaystyle 2^1 + 2^{1+1} + 2^{1+2}$

which equals to 14 and is divisible by 7

Yes. Another way to see this is to factor : $\displaystyle 2^1+2^2+2^3=2^1(2^0+2^1+2^2)=2\times 7.$

Originally Posted by

**mark1950** $\displaystyle 2^2 + 2^{2+1} + 2^{2+2}$

which equals to 28 and is divisible by 7

Similarly, $\displaystyle 2^2+2^3+2^4=2^2(2^0+2^1+2^2)=2^2\times 7.$

Using this idea, can you show that 7 divides $\displaystyle 2^n+2^{n+1}+2^{n+2}$ ?

Originally Posted by

**mark1950** But is it correct to show it just like that?

You only showed that 7 divides $\displaystyle 2^n+2^{n+1}+2^{n+2}$ if $\displaystyle n=1$ or 2...